Summary of Solution Procedures |
 
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Summary of Solution Procedures |
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The first step in the solution is to evaluate the total stiffness matrix 
and the total mass matrix 
. As the frequency domain analysis is a restart from an initial static analysis, the initial static solution provides the required data.
An initial estimate is now made of the fluid/structure relative velocity distribution, and this is used to evaluate the drag linearisation coefficients 
and 
. This in turn leads to the evaluation of the hydrodynamic loading distribution. The Dynamic Solution (Eq.6) is solved to give a first approximation to the dynamic displacements 
, which are then used to update 
and 
. Dynamic Solution (Eq.6) is again assembled and solved. This continues until convergence is achieved, typically in relatively small number of iterations. The current drag force coefficients are now calculated, and Mathematical Background (Eq,9) is solved iteratively for the static displacements. Internal restoring forces and reactions corresponding to the total solution are finally evaluated, and the analysis concludes with the output of all solution variables.
After discretising the input wave spectrum a random sea analysis proceeds in a manner analogous to that for the regular wave case. The total structure stiffness and mass matrices, 
and 
, are first assembled as before. A first estimate for the distribution of standard deviation of relative velocity is now evaluated by looping over all the seastate harmonic components, using the wave particle velocity at each frequency as a first approximation to the unknown relative velocity at that frequency. Values of 
and 
at each integration point on the riser are then found. Using these values the dynamic motion equation, Dynamic Solution (Eq.6), is now assembled and solved at each of the component frequencies, and the results of each solution stored. When this sweep is concluded, the stored results are used to again evaluate the distribution of standard deviation of relative velocity, and this leads to new values of the linearisation coefficients. The sweep over all component frequencies is now repeated, and the process continues until relative velocity standard deviations from successive sweeps are almost identical. At this point a final sweep is performed, during which the final static solution is also calculated. Then at each harmonic the total solution for that harmonic is obtained, the corresponding internal restoring forces and reactions are calculated, and all of the solution variables for that harmonic are output as for the regular wave case. This completes the random sea analysis. The frequency domain postprocessor can be used at this point to generate required statistical measures from the results at the individual harmonics.